Air-Standard Aerothermodynamic Analysis of Gas Turbine Engines With Wave Rotor Combustion

Transcription

1 Air-Standard Aerothermodynamic Analysis of Gas Turbine Engines With Wave Rotor Combustion M. R. Nalim 1 Associate Professor Department of Mechanical Engineering, Indiana University-Purdue University Indianapolis, Indianapolis, IN H. Li Graduate Student Department of Mechanical Engineering, Purdue University, West Lafayette, IN P. Akbari Research Associate Department of Mechanical Engineering, Indiana University-Purdue University Indianapolis, Indianapolis, IN The wave rotor combustor can significantly improve gas turbine engine performance by implementing constant-volume combustion. The periodically open and closed combustor complicates thermodynamic analysis. Key cycle parameters depend on complex gas dynamics. In this study, a consistent air-standard aerothermodynamic model with variable specific heat is established. An algebraic model of the dominant gas dynamics estimates fill fraction and internal wave compression for typical port designs, using a relevant flow Mach number to represent wave amplitudes. Nonlinear equations for thermodynamic state variables are solved numerically by Newton Raphson iteration. Performance measures and key operating conditions are predicted, and a quasione-dimensional computational model is used to evaluate the usefulness of the algebraic model. DOI: / Introduction Significant efficiency improvement is theoretically possible using pressure-gain combustors for gas turbines and jet engines 1. Pressure gain can be achieved by confining the combustion mixture or by promoting detonation, with examples in pulse combustors 1, wave rotor combustors 2, and pulse detonation engines PDEs 3. While the PDE relies on the inherent properties of a detonation wave, constant-volume combustion in wave rotor combustors relies mainly on mechanical confinement 4. Deflagrative pulsed combustion was employed in the earliest known gas turbine 5 and the V-1 buzz bomb. An inherent challenge of pulsed combustion is integration with nozzles, inlets, and turbines that prefer steady flow 3. The wave rotor combustor integrates relatively well with turbomachinery and benefits from internal compression, as explained below. First developed as a pressure-exchange device, the wave rotor has been demonstrated 6 as a combustion device. Computational fluid dynamics CFD models 7 can determine varying gas properties on the inlet and outlet planes and integrate them over a cycle to estimate pressure gain. At a simpler level, purely 1 Corresponding author. Manuscript received August 28, 2008; final manuscript received November 22, 2008; published online June 9, Review conducted by Dilip R. Ballal. thermodynamic analyses provide quick assessment of engine performance, but ignore gasdynamic constraints. Previous analytical models 8,9 have considered thermodynamic or particular gasdynamic cycles of pressure-exchange wave rotors, rather than onrotor combustion. CFD models are necessarily specific in geometric and physiochemical features, and not as broadly applicable. It is desirable to establish an analytic aerothermodynamic model with the gasdynamic and energetic characteristics of the wave rotor combustor, providing realistic performance and thermal data for engine configuration design and operation. This study establishes a consistent air-standard aerothermodynamic model evolved from previous models 10. It specifically includes the dominant gas dynamics of the wave rotor combustor, with complex fluid losses represented by wave process efficiencies. Real gas caloric behavior is represented by a polynomially temperature-dependent specific heat, c p T. Important engine performance parameters, temperature, and pressure data are evaluated as functions of an independent gasdynamic parameter that represents the primary wave amplitude in the rotor. CFD predictions are presented for some wave rotor cycles and combustion modes in a limited range of parameters to complement the predictions of the analytic model. 2 Wave Rotor Combustor Although pressure-exchange wave rotors were commercialized decades ago 11, wave rotor combustors have been investigated only in recent years. Predicted potential for gas turbines and stand-alone engines led to experiments by General Electric GE in the early 1960s 2, and a successful demonstration by Asea Brown Boveri ABB in Switzerland in the early 1990s 6. Both efforts highlighted needed improvements, mainly in mechanical design. A recent rig design by Rolls Royce awaits testing Wave Rotor Geometry and Working Principle. A wave rotor combustor consists of several combustion channels on a drum that rotates between two stationary end plates 2. By rotation, each channel is periodically charged and discharged as it rotates past properly sized and timed inlet and outlet ports. When recharged with combustible mixture and closed, combustion is initiated and completed within the channel. Mechanical confinement of combustion gas in a fixed channel volume allows relatively even pressure rise by deflagrative combustion, but detonative or intermediate modes of combustion are also possible 4. The flows in the manifolds ducts connected to the inlet/outlet ports are nearly steady, while rotor channel flow and combustion are inherently nonsteady a key advantage of the wave rotor configuration 2. The general model of gasdynamic processes inside the rotor channels used here is illustrated in Fig. 1, a simple schematic wave diagram of the typical outflow-inflow-combustion cycle in the wave rotor, with the common gas turbine and compressor shown schematically. Indispensable for cycle depiction, the wave diagram represents the time history of wave processes in each rotor channel as it rotates. Simplified pictorial depictions of three selected channels are shown at key reference states during the cycle of operation, and the trajectories of important waves are shown as various lines. Details of the combustion process are not shown; it is assumed to be completed under fixed volume. The focus is on the inflow-outflow gas dynamics that significantly influences the overall thermodynamic outcome. Unlike many other pulse combustion systems and PDEs, the wave rotor combustor operation is characterized by internal wave compression and expansion processes due to exit valving. Atmospheric air State 1 is compressed conventionally and enters the wave rotor State 2 with fuel. Discharged burned gas State 3 is expanded in a turbine to ambient pressure State 4. Each channel undergoes filling, initiation and completion of combustion, and blowdown of the pressurized gas to the turbine. Following combustion, high-pressure gas is expelled when the right Journal of Engineering for Gas Turbines and Power SEPTEMBER 2009, Vol. 131 / Copyright 2009 by ASME

2 Fig. 1 Wave pattern in a developed view of the wave rotor combustor end of the channel opens to the exhaust port, creating an expansion wave that travels to the left. As pressure falls, the left end of the channel opens to the inlet port, admitting combustible mixture. While filling continues, the scavenging of burned gas through the exit port is stopped by closing the exhaust port, generating a compressive wave or hammer shock. The residual gas and fresh air-fuel mixture State A trapped in the channel are favorably compressed by this shock wave, which propagates toward the inlet end wall. With both ends of the channel closed, the mixture is ignited. Confined combustion increases the pressure and temperature in the channel to State B, with any residual gas moderating the pressure gain. Every channel undergoes exactly the same cycle in phase with its angular location, providing relatively steady flow at any port location. A variety of cyclic flow and wave patterns are possible, depending on port timing, fuel distribution, and combustion modes 2. In particular, flammability limits dictate nonuniform fuel distribution resulting in stratified combustion and leaves either hot burned residual gas or cold unburned gas within the channels. This work presents an algebraic model for the case of burned residual gas, providing periodic solutions for a wide range of wave amplitudes and residual gas fraction, down to the limit of zero fill with no pressure gain. 3 Aerothermodynamic Cycle Analysis Air-standard cycles often assume either a homogeneous control-mass closed system e.g., Otto cycle, or steady-flow control-volume component open systems e.g., Brayton cycle. Oddly, the wave rotor combustor is characterized by nonsteady wave processes in nonhomogeneous fluid and by periodically open and closed phases. Nalim 10 provided a generalized thermodynamic model for pressure-gain combustors, considering internal losses and the buffering effect of residual gas. Their model s independent parameters fill fraction and wave compression are linked in the present aerothermodynamic model to a single independent variable, using the theory of characteristics and shock waves. 3.1 Assumptions. The conventional combustor in an unrecuperated gas turbine is replaced by the wave rotor, while the compressor and turbine are retained, with fixed adiabatic efficiencies. Wave rotor internal compression and expansion are also assigned adiabatic efficiencies to account for internal friction, shock losses, gradual opening/closing losses, and nonuniform port-mixing losses, by associating inflow with compression and outflow with expansion. Heat and leakage losses are neglected, consistent with adiabatic treatment of the turbomachinery. Combustion is treated as an external heat addition, and the working fluid is standard air 13 with c p T = T T T 3 kj/kg/k, T in kelvin. While the thermodynamic cycle is constructed on a calorically-true air-standard basis using this formulation consistently, the gasdynamic model assumes locally linear caloric behavior. 3.2 Analytical Procedures. The compressor inlet state is assumed as atmospheric stagnation temperature T 1t and stagnation pressure P 1t, and its adiabatic efficiency c and pressure ratio c = P 2t / P 1t are prescribed. The compressor discharge stagnation temperature T 2t is determined 14 using Newton Raphson iteration 15 to solve nonlinear polynomial equations. The wave rotor cyclic wave pattern and ideal pressure gain depend on port timings and boundary conditions, and on mixture composition and combustion characteristics. This study, condensed here from a more detailed report 16, considers a simple wave pattern amenable to algebraic modeling, characterized by a single independent gasdynamic variable outflow Mach number that controls fill fraction,, and wave amplitudes of compression and expansion. It uses a simplified representation of the exhaustport wave dynamics, leaving more complex cycles to be analyzed with CFD modeling. Assuming thorough mixing of channel gases during combustion for conservative performance estimation 10, any residual gas will originate from mixed burned gas at postcombustion State B. We assume further that residual gas expands isentropically from State B to ra assigning equivalently any irreversibility to the exiting gas expansion process. Thus, the mass conservation of ideal gases gas constant, R during combustion in a fixed volume requires P A T A + 1 T ra = T B = T P B B T B exp c p T RT T dt ra 1 Conservation of energy requires heat addition evaluated for the trapped channel mass to equal that over the entire combustor as an open system T B T B T 3t c v T dt + c v T dt = c p T dt 2 T A 1 T ra T2t For chosen combustor inlet and exit total temperatures T 2t and T 3t, these mass and energy equations involve four unknowns, T A, T ra, T B, and. To close the analysis, we seek additional relationships below to obtain estimates of and T B based on the gas dynamics of the exhaust and filling processes. The initial rotor exit Mach number M 3 is selected as an independent parameter, and distinguished from a port average M 3avg. Note that a low value of M 3 corresponds to a weak outflow expansion wave, and thus both a weak hammer shock and a low fill fraction, tending to Brayton-cycle constant-pressure combustion in the limit, as M 3 0. Assuming constant port static pressure and entropy, static temperature T 3 is calculated iteratively from T 3t and M 3avg. M 3avg,, and T B are estimated based on a model of gas dynamics and port timing greatly simplified by iteratively estimating a mean specific heat ratio,, for the expansion process only, with / Vol. 131, SEPTEMBER 2009 Transactions of the ASME

3 out contradicting the fidelity of the overall thermodynamic analysis to air-standard caloric relations. Sound speed, a, and velocity, u, across an isentropic expansion wave are related by a Reimann invariant equation of one-dimensional unsteady gas flow 8 u B + 2a B 1 = u 3 + 2a 3 1 T B = T M Although determined by approximate gas dynamics, this estimate of T B anchors a particular thermodynamic cycle that will be constructed on a calorically-true air-standard basis. Other properties at State B are derived from calorically-true air-standard relations to States 3 and 3t. The expansion wave fan has wave speed a B at its leading edge, and initially a 3 u 3 at its trailing edge. Upon reflection after traversing the channel length, L, the wave speed of the reflected leading edge changes as it passes through the wave fan from a B initially to a 3 +u 3. Using a linear average for the variable speed region, the intersection location, x, of the reflected leading edge with the initial trailing edge, and arrival time of the reflected leading edge, t lead, are, respectively x = L a B a 3 + u 3 a B + a 3 + u 3 a B a B +3a 3 u 3 4 t lead = L x + a B a B + a 3 + u 3 /2 + L x a 3 + u 3 For M 3 0.9, this estimate of t lead is found to be within 1% of an exact analytical calculation reported in Ref. 8. A similar assumption is made to estimate the time of arrival of the reflected trailing edge of the fan as t trail = L x x + a 3 u 3 a C + a 3 u 3 /2 + L with a C 5 1 a C = a M being the speed of sound in the simple wave region C behind the reflected expansion, estimated using the appropriate Reimann invariant. The exit port is assumed to close when the exit velocity reaches zero at t 3, taken to be the simple average of t lead and t trail. Furthermore, we assume a linear exit velocity profile between u 3 at t lead and zero at t 3 to define M 3avg such that it predicts mass flow equivalently in the exit port. The computed M 3avg is compared with the nominal value specified as a parameter, and the calculation is iterated to improve the estimates of T B and M 3avg. The fill fraction is the ratio of outflow mass to channel mass = 3M 3avg a 3 t 3 = P 3 T B t trail + t lead a 3 t lead + t trail t lead /4 M 3 B L P B T 3 2L t lead + t trail t lead /2 6 The remaining unknowns T A and T ra are determined by twodimensional Newton Raphson iteration of mass and energy conservation, with evaluation of the Jacobian matrix of the functions. The pressure ratios for adiabatic internal compression and expansion are obtained by applying isentropic efficiencies WC and WE to the internal compression and expansion processes, respectively, and the combustor pressure gain P 3t / P 2t is determined. Turbine specific work is calculated, applying a given turbine efficiency, t, and the cycle performance is determined. 4 Application For illustration, the above methodology is applied to a wave rotor combustor retrofit of a commercial small gas turbine: the Capstone C-60 microturbine engine, with manufacturer-estimated c =4.8, T 3t =1227 K, c =83%, t =85%, with T 1t =300 K, and assumed wave rotor internal efficiencies. Fig. 2 Efficiency,, and specific work, w, as functions of wave rotor combustor exit Mach number for different wave rotor internal efficiencies 4.1 Wave Rotor Combustion Effect on Existing Engine. Design of a wave rotor combustor for this engine assumes fixed P 2t, T 2t, and T 3t, and a resized turbine for flow matching. As design parameter M 3 increases from zero no filling to near unity choked condition, a stronger expansion fan with larger pressure drop P B / P 3t and larger positive flow work generates correspondingly higher wave compression pressure ratio WC = P A / P 2t and larger inlet flow work due to the stronger hammer shock. Fixed heat addition at higher temperature and larger fill fraction, causes higher overall pressure ratio, = P 3t / P 2t. Conversely, as M 3 0, all wave amplitudes die out, 0, and the cycle degenerates to the Brayton cycle. The effect of and WC predicted by simpler thermodynamic models 10 is confirmed, but the aerothermodynamic model illustrates how these two parameters tend to work together, rather than independently. An effective gasdynamic cycle design must provide both strong wave action and high fill fraction. Overall cycle performance metrics are shown in Fig. 2, for internal efficiencies WC = WE =0.85 or 0.75, for each calculation. Compression and expansion efficiencies have significant impact on overall performance, highlighting the need for better understanding of wave rotor loss mechanisms using detailed CFD modeling and experiments. 4.2 Effect of Combustor Heat Addition Temperature Ratio. The combustor fuel burn and consequent temperature increase will vary for off-design operating conditions and for other engines. Performance metrics are shown in Fig. 3, as the combustor temperature ratio varies between 2.0 and 3.5, for fixed compressor outlet conditions with internal efficiencies assumed at 80% and M 3 set to 0.6. The fuel-air mass ratio is varied to match an average fuel heating value. Unlike in the ideal Brayton cycle, where cycle efficiency is a direct function of compressor pressure ratio, the wave rotor combustor increases gains with more heat input, due to its pressure gain. Different combustor designs should be evaluated for a given combustor temperature ratio. 5 Computational Model Using the results of the algebraic model as a guide, CFD is used to investigate more complex and realistic gasdynamic and combustion features, and to provide quantitative predictions for specific rotor and port geometry. CFD models should be selected judiciously, depending on knowledge of grid-scale physics. Detailed model features cannot be validated until equally detailed experimental observations are available. Measurements of the unsteady gas dynamics in a pressure-exchange wave rotor have been recently used 17 to validate a quasi-one-dimensional unsteady Journal of Engineering for Gas Turbines and Power SEPTEMBER 2009, Vol. 131 /

4 Fig. 3 Cycle efficiency, specific work, and pressure gain as functions of temperature ratio with M 3 =0.6, WE = WC =0.8 flow code NASA-Q1D with comprehensive loss modeling 7,18 and a simple combustion model. This simplified CFD model differs from the presented algebraic model in the following aspects. a The port timing and boundary conditions can be set arbitrarily without simplistic wave patterns or uniform flow assumptions, but require significant judgment, experience, and creativity, for example, allowing the designer b c d e to optimize port opening and closing to maximize wave compression and fill fraction. Different timing and combustion models are used, and there is no large-scale mixing of postcombustion gases affecting residual gas density and fill fraction. The algebraic model is indifferent to combustion rate and assumes uniform overlean combustible mixture. In the CFD model, a minimally flammable mixture with an equivalence ratio of 0.7 is required, and thus requires the channel mixture to include dilution air apart from residual gas. The resulting thermal stratification strongly influences wave speeds, port timing optimization, mixing losses, and pressure gain. The flame speed depends principally on turbulent eddy diffusivity, assigned to be 1000 times the molecular diffusivity. The CFD model explicitly includes wall friction drag, shock losses, and port-mixing losses, while other losses modeled in the code were not activated. Loss effects are case dependent, unlike the assumed WC and WE of the algebraic model. Specific heat ratio is constant at =1.3, and the hydraulic diameter is set at 0.083L for estimating friction losses. An example CFD simulation is presented in Fig. 4 as computed contour plots or wave diagrams of nondimensional pressure, temperature, and fuel concentration as a function of time vertical axis for one cycle period. A plot of inflow and outflow velocity is also presented, leftmost. The temperature, pressure, and velocity are nondimensionalized by the combustor inlet stagnation state properties, T 2t, P 2t, and a 2t, respectively, while the fuel concentra- Fig. 4 CFD simulation of wave rotor combustor cycle with burned residual gas =0.76 and forward propagating deflagration in stratified fuel-air mixture / Vol. 131, SEPTEMBER 2009 Transactions of the ASME

5 tion is referenced to an equivalence ratio of Axial distance is nondimensionalized by channel length, L, and time by L/a 2t.A color scale bar is provided to the immediate right of each contour plot. The port and wall durations are indicated, respectively, by white and black vertical lines sidelining each contour plot. Following prior combustion the exit port opens with its static pressure set at 60% of inlet stagnation pressure, and generates an expansion wave that travels to the left, causing high speed outflow. As pressure falls at the inlet wall, the inlet port opens, and subsequently, the exit port closes, generating the hammer shock. The inlet port closes exactly when the hammer shock arrives, having supplied a stratified mixture that places fuel in flammable mixture near the inlet end wall and unfueled air in the remainder of the channel. Unlike in the algebraic model, neither outflow nor inflow is uniform see velocity plot, and neither precombustion nor postcombustion gases are uniform. When the exit port closes, the right side of the channel is occupied by residual hot gas, consisting of almost all the hot gas from stratified combustion in the previous cycle, much hotter than the equivalent burned residual of the algebraic model where the combustion gases mix fully in the channel. Hot residual gas degrades performance 11, and the highly nonuniform exit velocity and enthalpy flux profiles suggest a large mixing loss. The flame propagates forward from the igniter placed on the inlet-side end wall. The hot and cold gases are expelled when the exit opens again, and are assumed to fully mix in the exhaust duct to reach the required State 3t conditions. Fig. 5 Pressure-gain comparison of CFD and linear approximation to algebraic model 5.1 Summary of CFD Studies and Comparison With the Algebraic Model. Diverse cycle features 2 are possible with additional ports, nonuniform fuel-air mixtures, or different combustion modes and ignition methods. The computational study included cycles in which residual gas is unburned and relatively cold, obtained by limiting combustion to a downstream part of the channel. Although the main thermodynamic parameters of algebraic and CFD models are similar, the CFD model makes fewer simplifying assumptions and retains more detailed features, including significant kinetic energy and pressure imbalance in the gas at all times. Furthermore, the states identified as A and B in the algebraic model generally cannot be identified unambiguously in the CFD models, as the flow does not completely equilibrate in pressure nor at all in temperature. Wave compression pressure ratio, WC, is estimated from mass and energy conservation. However, equivalent compression and expansion efficiencies cannot be determined, except for the cases of 1. With these caveats in mind, the data from ten CFD solutions for combustion with burned residual gas six cases and unburned residual gas four cases were examined. They all involve stratified fresh mixture, in contrast to the uniform mixture assumed in the algebraic model. The overall temperature ratio is maintained at T 3t /T 2t = , and a range of exit static pressure and port timings are used to obtain varying. WC and were independent parameters in earlier purely thermodynamic models 10, but gas dynamics drives both up at higher flow Mach numbers. For burned residual gas, their correlations were positive but different for CFD and algebraic methods. Stratified burned and cold gas layers in the CFD model multiply and delay the wave reflections, and dictate different port timings, as exit velocity gradually decreases and weakens the hammer shock. The algebraic model was exercised for constant =1.3 and WC =0.73 and WE =0.86 efficiencies derived from a fully purged CFD case with the same combustion direction as the burned-gas residual CFD cases. Comparison of the algebraic and CFD calculations of performance must consider the combined influence of cycle parameters. A useful linear extension of the dependence of on parameters WC and can be extracted from the algebraic model by approximating the algebraic solution with a linear multivariate regression fit. Such a correlation is potentially useful for design guidance, and can be tested for validity using CFD prediction for similar cases. The algebraically predicted pressure gain was analyzed using standard statistical regression techniques available in a spreadsheet software program and found to be approximated well correlation coefficient by a linear fit = WC. The limited number of CFD cases with burned residual gas and forward combustion propagation are tested against this prediction in Fig. 5 small diamond markers. Although they lie in a different region of the - WC space, the computed pressure gain of the burned residual CFD cases are reasonably well matched with the predictions of the linearly-extended algebraic model. This correlation allows the predictions of the algebraic model to be extended to wider gasdynamic regimes, if the residual gas density is comparable to algebraic model assumptions. Much of the deviation from fit to the CFD model may be due to variations in wave compression and expansion efficiency that are difficult to estimate. Also shown in Fig. 5 are the same comparison for the CFD cases of unburned gas residual backward flame propagation and no residual both forward and backward propagations. Itisunsurprising that the correlation is poor for unburned residual gas, as this contradicts an important assumption of the present algebraic model. A separate model for unburned residual gas cycles may allow a parallel correlation to be established. 6 Conclusions A consistent air-standard aerothermodynamic algebraic analysis is applied to the wave rotor combustor, using the theory of characteristics and shock waves and variable specific heat. As wave amplitudes, fill fraction, and degree of combustion confinement vary with an independent design parameter, the model evaluates the combustor pressure gain and cycle performance. Furthermore, an existing wave rotor combustor CFD model is exercised to evaluate algebraic model applicability. Although the linkage between wave compression and fill fraction in the CFD model is different from the algebraic model, the general performance trends, as a function of these variables, are similar. Analytic predictions that a fully purged wave rotor combustor could provide a nominal 60 kw microturbine with nearly 40% pressure gain and 30% fuel savings are consistent with CFD analysis allowing shock, friction, gradual opening, and portmixing losses, but additional losses must be considered. Nomenclature a speed of sound m/s Journal of Engineering for Gas Turbines and Power SEPTEMBER 2009, Vol. 131 /

6 c p and c v constant-pressure and constant-volume specific heats kj/kg/k L channel length m M Mach number P pressure Pa R gas constant kj/kg K T temperature K t port open time s w specific work kj/kg-air u velocity m/s fill fraction pressure ratio efficiency specific heat ratio Subscripts A state before combustion B state after combustion C state after reflected expansion wave c compressor r residual gas t stagnation state total property WC wave compression WE wave expansion References 1 Kentfield, J. A. C., and O Blenes, M., 1988, Methods for Achieving a Combustion-Driven Pressure Gain in Gas Turbines, ASME J. Eng. Gas Turbines Power, 110 4, pp Akbari, P., and Nalim, M. R., 2009, Recent Developments in Wave Rotor Combustion Technology and Future Perspectives: A Progress Review, J. Propul. Power, in press. 3 Roy, G. D., Frolov, S. M., Borisov, A. A., and Netzar, D. W., 2004, Pulse Detonation Propulsion: Challenges, Current Status, and Future Perspective, Prog. Energy Combust. Sci., 30 6, pp Nalim, M. R., 1999, Assessment of Combustion Modes for Internal Combustion Wave Rotors, ASME J. Eng. Gas Turbines Power, 121 2, pp Stodola, A., 1927, Steam and Gas Turbines, Vol. 2, McGraw-Hill, New York,. 6 Walraven, F., 1994, Operational Behavior of a Pressure Wave Machine With Constant Volume Combustion, ABB Technical Report No. CHCRC Nalim, M. R., 2000, Longitudinally Stratified Combustion in Wave Rotors, J. Propul. Power, 16 6, pp Resler, E. L., Moscari, J. C., and Nalim, M. R., 1994, Analytic Design Methods for Wave Cycles, J. Propul. Power, 10 5, pp Akbari, P., Müller, N., and Nalim, M. R., 2006, Performance Enhancement of Microturbine Engines Topped With Wave Rotors, ASME J. Eng. Gas Turbines Power, 128 1, pp Nalim, M. R., 2002, Thermodynamic Limits of Work and Pressure Gain in Combustion and Evaporation Processes, J. Propul. Power, 18 6, pp Akbari, P., Nalim, M. R., and Müller, N., 2006, A Review of Wave Rotor Technology and Its Applications, ASME J. Eng. Gas Turbines Power, 128 4, pp Matsutomi, Y., Hein, C., Lian, C., Meyer, S., and Heister, S., 2007, Facility Development for Testing of Wave Rotor Combustion Rig, AIAA Paper No Cengel, Y. A., and Boles, M. A., 2005, Thermodynamics: An Engineering Approach, 5th ed., McGraw-Hill, New York. 14 Sarabchi, K., 2004, Performance Evaluation of Reheat Gas Turbine Cycles, Proc. Inst. Mech. Eng., Part A, 218 7, pp Chapra, S. C., and Canale, R. P., 2001, Numerical Methods for Engineers: With Software and Programming Application, 4th ed., McGraw-Hill, New York. 16 Nalim, M. R., Li, H., and Akbari, P., 2009, Air-Standard Aerodynamic Analysis of Gas Turbine Engines With Wave Rotor Combustion, ASME Paper No. GT Wilson, J., Welch, G. E., and Paxson, D. E., 2007, Experimental Results of Performance Tests on a Four-Port Wave Rotor, AIAA Paper No Paxson, D. E., 1997, A Numerical Investigation of the Startup Transient in a Wave Rotor, ASME J. Eng. Gas Turbines Power, 119 3, pp / Vol. 131, SEPTEMBER 2009 Transactions of the ASME